In post 17730 I wrote:
"Jeff has a bunch of really good blog posts about directional couplers."
Here's the blog post I was thinking of but could not find:
That's an excellent analysis of the Tandem Match.
This business of adding a voltage reading to a current reading (with proper scaling)
is the basis of most SWR meters that an amateur radio operator might use.
It is also an excellent example of how circuit analysis
of a rather difficult problem can be carried out.
And gives further insight to the nature of reflections.
Note that the nanovna can measure an arbitrary complex impedance
within the range of the instrument.
And that from complex impedance, we can compute the SWR
for any desired characteristic impedance, perhaps 450 ohm ladder line.
As Jeff shows, a Tandem Match is only useful in a 50 ohm environment,
as determined by the 50 ohm resistors that are typically stuffed.
Jerry, KE7ER
On Sun, Sep 27, 2020 at 11:04 AM, Jerry Gaffke wrote:
....
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Allow me a short rant here, as I find the subject interesting,
and key to understanding what a nanovna is.
Composing this note helped me to think about it.
The key passages of the Bruene article
are on the first page:
#######################################
Textbooks tell us that the voltage on a line can be considered to have two
components, a forward component ... and a reflected component.
#######################################
An important thing to note is that at any point along the line the reflected
components of voltage and current are exaclty 180 degrees out of phase.
#######################################
How the Directional Coupler Works
The directional coupler can sense either the forward or reflected component by
taking advantage of the fact that the reflected components of voltage and
current are 180 degrees out of phase while the forward components are in
phase. A small voltage derived from the current in the line is added to a
sample of the voltage across the line. If these two samples have the right
amplitude relationship, the two reflected components cancel. The sum then
represents only the forward component. By reversing the phase of the current
sample 180 degrees, the forward components cancel and the result is the sum of
only the reflected components.
#######################################
Those first two items are stated as known textbook facts,
Bruene does not attempt to explain why they are true.
Here is one way to go about it:
Think about 5 volts DC into a 50 ohm resistive load, we would measure 5v/50 =
0.1 amps into the load.
And the power burned by that 50 ohms would be 5*0.1 = 0.5 Watts.
Assume we apply 5 volts DC to a black box, and we measure -0.1 amps, which is
to say that the
current is flowing the opposite direction. This means there is something
unexpected about the box,
it is somehow sending 0.5 watts in the opposite direction down our wire toward
the 5 volt battery.
Perhaps the box has a 10 volt battery inside, in series with a 50 ohm
resistor.
That works for AC as well as DC, we might have 0.1 amps rms travelling from
the black box to
a 10mhz 5 volt rms signal source. The black box in this case would have to
contain a second
10mhz source that is exactly synchronized with our 5 volt rms source.
We can have 10 mhz signals travelling in both directions simultaneously, as is
the case when
the black box reflects part of the 10mhz energy back to the signal source.
At this point we have caught up with Bruene, being able to differentiate
forward power from reverse power
by noting that reverse power has voltage and current that are 180 degrees out
of phase.
The other curiosity in the Bruene article is that these SWR meters add RF
voltage to RF current,
which makes about as much sense to a physicist as adding bananas to miles.
For a result of power in watts we would have to multiply voltage and current,
but you can't do a multiply with coils and caps and resistors.
Let's think again about our 5 volts DC driving a 50 ohm resistor, resulting in
a 5/50 = 0.1 amp current.
Assume we measure the 0.1 amp current by passing it through a 1 ohm resistor,
resulting in 0.1*1 = 0.1 volts across it.
And assume we scale the 5 volts down to 0.1 volts by passing it through a
resistive divider of 49 + 1 ohms in series.
Now, if we add the 0.1 volt current reading to the 0.1 volt voltage reading,
we get 0.2 volts, but only if the resistor is 50 ohms.
And if the current is going in the wrong direction, we get zero volts when we
add the two readings.
If we have currents going in both directions simultaneously, all we see is the
forward component.
Jerry, KE7ER
A minor correction: On Sun, Sep 27, 2020 at 11:12 AM, Jerry Gaffke wrote:
Differentiating between the "currents going in both directions"
doesn't work so well in the case of DC, we need AC signals for that.
